**Authors:** Attilio Colombo

The intent of this work is to present a discussion of the Galilean Principle of Relativity and of its implications for what concerns the characteristics of light propagation and the nature of simultaneity. It is shown that by using a clock synchronization procedure that makes use of isotropically propagating signals of generic nature, the simultaneity of distinct events can be established in a unique way by different observers, also when such observers are in relative motion between themselves. Such absolute nature of simultaneity is preserved in the passage from a stationary to a moving reference frame also when a set of isochronous generalized coordinates is introduced. These transformations of coordinates can be considered as a generalization of the Lorentz transformations to the case of synchronization signals having characteristic speed different from the speed of light in vacuum. The specific invariance properties of these coordinate transformations with respect to the characteristic speed of propagation of the synchronization signals and of the corresponding constitutive laws of the underlying physical phenomenon are also presented, leading to a different interpretation of their physical meaning with respect to the commonly accepted interpretation of the Lorentz transformation as a space-time distortion. On the basis of these results, the emission hypothesis of W. Ritz, that assumes that light is always emitted with the same relative speed with respect to its source and that is therefore fully consistent with the Galilean Principle of Relativity, is then applied to justify the outcomes of the Michelson-Morley and Fizeau interferometric experiments by introducing, for the latter case, an additional hypothesis regarding the possible influence of turbulence on the refractive index of the fluid. Finally, a test case to verify the validity of either the Galilean or the Relativistic velocity composition rule is presented. The test is based on the aberration of the light coming from celestial objects and on the analysis of the results obtained by applying the two different formulas for the resultant velocity vector to process the data of the observed positions, as measured by a moving observer, in order to determine the actual un-aberrated location of the source.

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[v1] 2019-03-10 12:45:13

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